.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemkl_lapack-singular-value-eigenvalue-routines: LAPACK Singular Value and Eigenvalue Problem Routines ===================================================== .. container:: LAPACK Singular Value and Eigenvalue Problem routines are used for singular value and eigenvalue problems, and for performing a number of related computational tasks. The following table lists the LAPACK Singular Value and Eigenvalue Problem routine groups. .. container:: tablenoborder .. list-table:: :header-rows: 1 * - Routines - Scratchpad Size Routines - Description * - :ref:`onemkl_lapack_gebrd` - :ref:`onemkl_lapack_gebrd_scratchpad_size` - Reduces a general matrix to bidiagonal form. * - :ref:`onemkl_lapack_gesvd` - :ref:`onemkl_lapack_gesvd_scratchpad_size` - Computes the singular value decomposition of a general rectangular matrix. * - :ref:`onemkl_lapack_heevd` - :ref:`onemkl_lapack_heevd_scratchpad_size` - Computes all eigenvalues and, optionally, all eigenvectors of a complex Hermitian matrix using divide and conquer algorithm. * - :ref:`onemkl_lapack_hegvd` - :ref:`onemkl_lapack_hegvd_scratchpad_size` - Computes all eigenvalues and, optionally, all eigenvectors of a complex generalized Hermitian definite eigenproblem using divide and conquer algorithm. * - :ref:`onemkl_lapack_hetrd` - :ref:`onemkl_lapack_hetrd_scratchpad_size` - Reduces a complex Hermitian matrix to tridiagonal form. * - :ref:`onemkl_lapack_orgbr` - :ref:`onemkl_lapack_orgbr_scratchpad_size` - Generates the real orthogonal matrix :math:`Q` or :math:`P^T` determined by gebrd. * - :ref:`onemkl_lapack_orgtr` - :ref:`onemkl_lapack_orgtr_scratchpad_size` - Generates the real orthogonal matrix :math:`Q` determined by sytrd. * - :ref:`onemkl_lapack_ormtr` - :ref:`onemkl_lapack_ormtr_scratchpad_size` - Multiplies a real matrix by the orthogonal matrix :math:`Q` determined by sytrd. * - :ref:`onemkl_lapack_syevd` - :ref:`onemkl_lapack_syevd_scratchpad_size` - Computes all eigenvalues and, optionally, all eigenvectors of a real symmetric matrix using divide and conquer algorithm. * - :ref:`onemkl_lapack_sygvd` - :ref:`onemkl_lapack_sygvd_scratchpad_size` - Computes all eigenvalues and, optionally, all eigenvectors of a real generalized symmetric definite eigenproblem using divide and conquer algorithm. * - :ref:`onemkl_lapack_sytrd` - :ref:`onemkl_lapack_sytrd_scratchpad_size` - Reduces a real symmetric matrix to tridiagonal form. * - :ref:`onemkl_lapack_ungbr` - :ref:`onemkl_lapack_ungbr_scratchpad_size` - Generates the complex unitary matrix :math:`Q` or :math:`P^T` determined by gebrd. * - :ref:`onemkl_lapack_ungtr` - :ref:`onemkl_lapack_ungtr_scratchpad_size` - Generates the complex unitary matrix :math:`Q` determined by hetrd. * - :ref:`onemkl_lapack_unmtr` - :ref:`onemkl_lapack_unmtr_scratchpad_size` - Multiplies a complex matrix by the unitary matrix :math:`Q` determined by hetrd. .. toctree:: :hidden: gebrd gebrd_scratchpad_size gesvd gesvd_scratchpad_size heevd heevd_scratchpad_size hegvd hegvd_scratchpad_size hetrd hetrd_scratchpad_size orgbr orgbr_scratchpad_size orgtr orgtr_scratchpad_size ormtr ormtr_scratchpad_size syevd syevd_scratchpad_size sygvd sygvd_scratchpad_size sytrd sytrd_scratchpad_size ungbr ungbr_scratchpad_size ungtr ungtr_scratchpad_size unmtr unmtr_scratchpad_size